Simplify the following expression: $r = \dfrac{k}{7} + \dfrac{k}{3}$
Answer: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $7$ and $3$ $\lcm(7, 3) = 21$ $ r = \dfrac{3}{3} \cdot \dfrac{k}{7} + \dfrac{7}{7} \cdot \dfrac{k}{3} $ $r = \dfrac{3k}{21} + \dfrac{7k}{21}$ $r = \dfrac{3k +7k}{21}$ $r = \dfrac{10k}{21}$